How far ahead can I make summer rolls?

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Was planning to bring summer rolls as Christmas Day appetizer, for a family full of celiacs (thus avoiding the "you aren't allowed to eat this" issue). However, with a toddler in the house, it would be much, much easier if I could actually assemble the summer rolls the night before (approx 8pm) and refrigerate (til about noon the next day). Would that be do-able or would the rice paper wrappers get hard/soggy/something else inedible? If I covered with a damp towel?
Or would I be better served by doing "lettuce wraps" instead? I wanted to avoid the whole "make your own" thing...
Any thoughts (or other suggestions for easy, make ahead, GF appetizers)?